Exploiting the analytic properties of scattering amplitudes, we provide an alternative but equivalent definition of the standard Mellin transform used to obtain celestial correlation functions. From this representation, we identify a celestial dispersion relation that relates the reduced correlation function to the poles and discontinuities of the bulk amplitude, and we present a novel expansion for the celestial correlator from an integral transform of the Froissart-Gribov expansion on the bulk. By drawing an analogy with the standard CFT case, we define the celestial Regge limit and identify the relevant celestial CFT data in terms of the partial amplitudes governing the bulk Regge limit.

Brazil

Eduardo Casali

Italy

Riccardo Pozzi

Celestial Regge theory

On-shell kinematics for gluon scattering can be parametrized with points on the celestial sphere; in the limit where these points collide, it is known that tree-level gluon scattering amplitudes exhibit an operator product expansion (OPE)-like structure. While it is possible to obtain singular contributions to this celestial OPE, getting regular contributions from both holomorphic and anti-holomorphic sectors is more difficult. In this paper, we use twistor string theory to describe the maximal helicity violating (MHV) sector of tree-level, four-dimensional gluon scattering as an effective 2d conformal field theory on the celestial sphere. By organizing the OPE between vertex operators in this theory in terms of soft gluon descendants, we obtain all-order expressions for the celestial OPE which include all regular contributions in the collinear expansion. This gives new, all-order formulae for the collinear splitting function (in momentum space) and celestial OPE coefficients (in the conformal primary basis) of tree-level MHV gluon scattering. We obtain these results for both positive and negative helicity gluons, and for any incoming/outgoing kinematic configuration within the MHV sector.

United Kingdom

Tim Adamo

Wei Bu

United States

Atul Sharma

All-order celestial OPE in the MHV sector

Both celestial and momentum space amplitudes in four dimensions are beset by divergences resulting from spacetime translation and sometimes scale invariance. In this paper we consider a (linearized) marginal deformation of the celestial CFT for Yang-Mills theory which preserves 2D conformal invariance but breaks both spacetime translation and scale invariance and involves a chirally coupled massive scalar. The resulting MHV celestial amplitudes are completely finite (apart from the usual soft and collinear divergences and isolated poles in the sum of the weights) and take the canonical CFT form. Moreover, we show they can be simply rewritten in terms of AdS3-Witten contact diagrams which evaluate to the well-known D-functions, thereby forging a direct connection between flat and AdS holography.

Walker Melton

Andrew Strominger

Celestial amplitudes as AdS-Witten diagrams

We give an explicit realization of the 4d local operator / 2d conformal block correspondence of Costello and Paquette in the case of gauge theories. This is accomplished by lifting the 4d local operators to non-local operators in twistor space using a holomorphic generalization of the Wilson line. This procedure automatically constructs the 2d conformal blocks corresponding to the local operator. We interpret this lifting as effectively integrating out the 2d degrees of freedom living on the defect. We present some 2d chiral CFT representation of the defect algebra whose correlators reproduce the conformal blocks obtained by the lifting procedure.

The 4d/2d correspondence in twistor space and holomorphic Wilson lines

We compute the operator product expansions of gluons and gravitons in celestial CFT from the worldsheet OPE of vertex operators of four-dimensional ambitwistor string theories. Remarkably, the worldsheet OPE localizes on the short-distance singularity between vertex operator insertions which in turn coincides with the OPE limit of operator insertions on the celestial sphere. The worldsheet CFT dynamically produces known celestial OPE coefficients — as well as infinite towers of SL(2, ℝ) descendant contributions to the celestial OPE — without any truncations or approximations. We obtain these results for all helicities and incoming/outgoing configurations. Furthermore, the worldsheet OPE encodes the infinite-dimensional symmetry algebras associated with the conformally soft sectors of gauge theory and gravity. We provide explicit operator realizations of the currents generating these symmetries on ambitwistor space in terms of vertex operators for soft gluons and gravitons, also computing their actions on hard particles of all helicities. Lastly, we show that the worldsheet OPE for momentum eigenstates produces the collinear splitting functions of gluons and gravitons.

Celestial operator products from the worldsheet

Using the ambitwistor string, we compute tree-level celestial amplitudes for biadjoint scalars, Yang-Mills and gravity to all multiplicities. They are presented in compact CHY-like formulas with operator-valued scattering equations and numerators acting on a generalized hypergeometric function. With these we extend the celestial double copy to tree-level amplitudes with arbitrary number of external states. We also show how color-kinematics duality is implemented in celestial amplitudes and its interpretation in terms of a generalized twisted cohomology theory.

Celestial double copy from the worldsheet

Celestial amplitudes which use conformal primary wave functions rather than plane waves as external states offer a novel opportunity to study properties of amplitudes with manifest conformal covariance and give insight into a potential holographic celestial conformal field theory at the null boundary of asymptotically flat space. Since translation invariance is obscured in the conformal basis, features of amplitudes that heavily rely on it appear to be lost. Among these are the remarkable relations between gauge theory and gravity amplitudes known as the double copy. Nevertheless, properties of amplitudes reflecting fundamental aspects of the perturbative regime of quantum field theory are expected to survive a change of basis. Here we show that there exists a well-defined procedure for a celestial double copy. This requires a generalization of the usual squaring of numerators which entails first promoting them to generalized differential operators acting on external wave functions and then squaring them. We demonstrate this procedure for three- and four-point celestial amplitudes and give an argument for its validity to all multiplicities.

France

Andrea Puhm

Double Copy for Celestial Amplitudes

Color-kinematics duality is a remarkable conjectured property of gauge theory which, together with double copy, is at the heart of a wealth of new developments in scattering amplitudes. So far, its validity has been verified in most cases only empirically, with limited ab initio understanding beyond tree-level. In this paper we provide initial steps in a first-principle understanding of color-kinematics duality and double-copy at loop level, through a detailed analysis of the field-theory limit of the monodromy relations of string theory at one loop. In this limit, we dissect the type of Feynman graphs generated and the relations they obey. We find that graphs with contact-terms are unavoidable and are generated in the field theory limit of “bulk” contours which do not have a standard physical interpretation in string perturbation theory. We show how they are related to ambiguities in the definition of the loop momentum and that their role is precisely to cancel those ambiguities.

Sebastian Mizera

Piotr Tourkine

Loop amplitudes monodromy relations and color-kinematics duality

We reformulate the monodromy relations of open-string scattering amplitudes as boundary terms of twisted homologies on the configuration spaces of Riemann surfaces of arbitrary genus. This allows us to write explicit linear relations involving loop integrands of open-string theories for any number of external particles and, for the first time, to arbitrary genus. In the non-planar sector, these relations contain seemingly unphysical contributions, which we argue clarify mismatches in previous literature. The text is mostly self-contained and presents a concise introduction to twisted homologies. As a result of this powerful formulation, we can propose estimates on the number of independent loop integrands based on Euler characteristics of the relevant configuration spaces, leading to a higher-genus generalization of the famous (n − 3)! result at genus zero.

Canada

Monodromy relations from twisted homology

The D = 11 pure spinor superparticle has been shown to describe linearized D = 11supergravityinamanifestlycovariantway. Anumberofauthorshaveproposedthat its correlation functions be used to compute amplitudes. The use of the scalar structure of the eleven-dimensional pure spinor top cohomology introduces a natural measure for computing such correlation functions. This prescription requires the construction of ghost number one and zero vertex operators. In these notes, we construct explicitly a ghost number one vertex operator but show the incompatibiliy of a ghost number zero vertex operator satisfying a standard descent equation for D = 11 supergravity.